"The American people celebrated this bipartisan leadership. But, recently, we have noted that members on both sides of the aisle are calling for a return to earmarking. We believe this would be unwise and would further damage Congress' reputation and ability to tackle the nation's challenges," the senators wrote.

While there's no immediate jeopardy to the earmark moratorium, supporters would like to challenge it.

Senate Majority Whip Richard J. Durbin, who also serves as chairman of the Appropriations Subcommittee on Defense, has been one of the most vocal advocates for reviving the practice of congressionally directed spending.

"I'm opposed to that. I believe that we can reform this system, establish a means of local input as part of the Washington decision," the Illinois Democrat said Thursday, responding to the letter that Coburn and Udall are circulating.

"I do not want to turn over the decision on the future of projects in the state of Illinois to someone in Washington who is not familiar with our state, our economy and how we can build jobs in my state," Durbin said.

When Durbin recently made similar comments to a union crowd, reported by the Huffington Post , Speaker John A. Boehner, R-Ohio, was quick to reject the idea.

"I've expressed myself repeatedly," Durbin said. "I know there's support on both sides of the aisle."